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Full-name: PLMossman
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Subject: Re: [Colonial Numismatics] for CT Copper Collectors
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Explanation of Student's T test:=20
=20
Start: "The _t-statistic_ (https://en.wikipedia.org/wiki/T-statistic) was =
=20
introduced in 1908 by _William Sealy Gosset_=20
(https://en.wikipedia.org/wiki/William_Sealy_Gosset) , a chemist working fo=
r the _Guinness_=20
(https://en.wikipedia.org/wiki/Guinness) _brewery_=20
(https://en.wikipedia.org/wiki/Brewery) in _Dublin_ (https://en.wikipedia.=
org/wiki/Dublin) , _Ireland_=20
(https://en.wikipedia.org/wiki/Ireland) " (Student was his _pen name_=20
(https://en.wikipedia.org/wiki/Pen_name) ) [A fascinating story]=20
=20
The Student's t test is widely used in medicine and elsewhere to determine =
=20
the effectiveness of new procedures - whether one medicine, procedure, or=
=20
treatment, etc. is better than a control or the "old way." A t test value=
=20
of 1.0 =3D identical results; values from 0.999 to 0.051 mean the two=20
comparisons are similar, or you can't be sure the values are different or =
that=20
your new idea is working.
But a value of 0.05 level or smaller is a positive result that the compared=
=20
entities are different - or that the new procedure is working, etc.
=20
So in discussing the relative weights of [96] 1783 and [165] 1785 Novas,=
=20
I took my data from pages 141-44, note 186, and Table 5.5 From Crime to=20
Punishment.
=20
Quote "The important thing to note is that these nine varieties of Nova=20
coppers were not consistently struck from the same planchet stock. Absence=
of=20
a homogeneous weight suggests no common weight standard with the=20
1783-dated group being significantly heavier that the 1785 varieties."=20
=20
See Table 5.5, [copied below] where I asked statistically two questions=20
about 1785 4-D.
First: whether the average weights of 1785 4-D [124.52 =C2=B1 7.37] is si=
milar=20
to the three in the 1783 group, [123.69 =C2=B1 10.70.],
Answer: Student=E2=80=99s T test: p =3D 0.72;=20
p means probability.
Answer: First Question:=20=20
=20
That means that there are 72 chances in 100 that 1785 4-D and all of 1783=
=20
Nova are the same weight. [Read ?? maybe the same planchet stock,] =
=20
Second question: whether 4-D, 124.52 =C2=B1 7.37, was similar in weight t=
o=20
other five 1785-dated varieties, [115.0=C2=B16.8] Student=E2=80=99s T tes=
t: p =3D 1.7 x=20=20
10-9.
Answer - Student=E2=80=99s T test: p =3D 1.7 x 10-9.=20
That means that the likelihood of the average weights of the single 1785=20
group 4-D being similar to the other five 1785 varieties is 0.00000000017=
=20
chances. Pretty slim pickins!=20=20
I am not a mathematician - I have friends who are and I just love=20
Microsoft Excel!! I've told you all I know.=20
Enjoy,=20=20
Phil=20
=20
=20
In a message dated 8/11/2015 7:52:20 A.M. Eastern Daylight Time,=20=20
colonial-coins@yahoogroups.com writes:
=20
=20
=20
Thanks Craig,=20=20
That link about Student t-test makes it perfectly clear... NOT! It's=20
Greek to me. Knowing it's some statistical formula, any attempt to explai=
n is=20
probably useless. Telling me that the difference between the average of=20
two varieties is X grains or is 6% would be something I can comprehend. =
=20
Ray=20
=20
On Mon, Aug 10, 2015 at 10:47 PM, Cmcdon0923 CMcdon0923@aol.com=20
[colonial-coins] wrote:=20=20
Yeah.....this makes it so much clearer .....=20
_https://en.m.wikipedia.org/wiki/Student%27s_t-test_=20
(https://en.m.wikipedia.org/wiki/Student's_t-test)=20
Sent from my iPhone.....so spelling doens't count.=20
On Aug 10, 2015, at 9:17 PM, Ray Williams _njraywms@optonline.net_=20
(mailto:njraywms@optonline.net) [colonial-coins] <_colonial-coins@yahoogr=
oups.com_=20
(mailto:colonial-coins@yahoogroups.com) > wrote:
=20
Okay,=20
I'll bite... What is a Student's T test? Is this a statistical term that=
=20
I won't understand, not being a statistician?
Ray
=20
On Mon, Aug 10, 2015 at 09:02 PM, _PLMossman@aol.com_=20
(mailto:PLMossman@aol.com) [colonial-coins] wrote:=20=20
Hi Will:
My numbers re: undertypes are just statistical guesses - since the 20=20
identifiable undertypes are too few to make positive statements.=20
=20
In my Table 5.5 in From Crime to Punishment, I was able to gather over the=
=20
years weight stats on 96 1783s, and 165 1785s that did not appear=20
overstruck.=20
=20
=20=20=20=20=20
COIN
sample=20=20
average=20=20
st. dev.=20=20=20
1783 1-A=20=20
21=20=20
128.65=20=20
=C2=B110.47=20=20=20
1783 2-B=20=20
47=20=20
123.66=20=20
=C2=B112.05=20=20=20
1783 3-C=20=20
28=20=20
120.04=20=20
=C2=B16.42=20=20=20
group=20=20
96=20=20
123.69=20=20
=C2=B110.70=20=20=20
1785 1-B=20=20
26=20=20
119.39=20=20
=C2=B14.64=20=20=20
1785 2-A *=20=20
23=20=20
117.39=20=20
=C2=B14.43=20=20=20
1785 3-B=20=20
47=20=20
112.50=20=20
=C2=B16.60=20=20=20
1785 4-C *=20=20
17=20=20
111.81=20=20
=C2=B16.38=20=20=20
1785 4-D *=20=20
24=20=20
124.52=20=20
=C2=B17.37=20=20=20
1785 5-E *=20=20
28=20=20
114.90=20=20
=C2=B17.51=20=20=20
group=20=20
165=20=20
116.35=20=20
=C2=B17.56
Those with an * have been identified as 1788 CT host coins. [P.S. I have=
=20
a 56-n on a `1783 Nova]
=20
These Novas are not a homogeneous group: The 1785 Crosby 4-C and 4-D=20
varieties are significantly different in average planchet weight, Student=
=E2=80=99s T=20
test: p =3D 1.2 x 10-6=20=20
=20
1783 Crosby 3-C and 1785 Crosby 1-B are very similar in weight indicating=
=20
a common thread for this biennially paired obverse die. Student=E2=80=
=99s T=20
test: p =3D 0.68.=20
For 1785 4-D being similar to the total 1783 group, Student=E2=80=99s T te=
st: p =3D=20
0.72;=20=20
but for 4-D being similar to other 1785 varieties, Student=E2=80=99s T t=
est: p =3D=20
1.7 x 10-9.=20
It would appear that the lighter weight Novas, as a group, were favored as=
=20
host coins and fewer are to be found in circulation. Also consider the =
=20
fact that if Novas were bought in bulk by weight, the minter would get mor=
e=20
coins per barrel full to use as pre-made planchet hosts.=20=20=20=20
Lots of fun.=20
Best=20
Phil
=20
=20
=20
In a message dated 8/10/2015 5:25:28 P.M. Eastern Daylight Time,=20
_colonial-coins@yahoogroups.com_ (mailto:colonial-coins@yahoogroups.com) =
writes:
=20
=20
Phil,
It does definitely "feel" like something is going on, with 2-A, 4-C and=20
5-E showing up as undertypes, while 2-B (83) and 3-B don't. In the "Money"=
=20
note, you mention that 4-D is the rarest Nova. I believe that 2-A and 4-C=
=20
are the rarest of the non-1786 varieties. I also think that 1-B (85) may =
be=20
scarcer than 4-D. I have two sets of the 83/85 varieties (no 86), and a=20
few extras. 2-A and 4-C were definitely the hardest to find. I also have =
an=20
88 CT 12.2-C struck over 5-E Nova that probably wasn't in the census.
Will
Sent from my Verizon Wireless 4G LTE DROID
"_PLMossman@aol.com_ (mailto:PLMossman@aol.com) [colonial-coins]"=20
<_colonial-coins@yahoogroups.com_ (mailto:colonial-coins@yahoogroups.com) >=
wrote:
Hi Ray:
I would expect it. Note in From Crime to Punishment, pp. 141-44, note=20
192, and in Money 194-95, note 116, I found that the rarest intact Novas w=
ere=20
the most common host coins. There were not enough found to be=20=20
statistically significant, but there appears to be a trend. The same mater=
ial is in=20
both books.
Best
Phil
=20
=20
In a message dated 8/10/2015 12:50:29 P.M. Eastern Daylight Time,=20=20
_colonial-coins@yahoogroups.com_ (mailto:colonial-coins@yahoogroups.com) =
writes:
=20
Hi Phil,=20=20
The owner says it is a 1788 M4.1-K o/s on a 1785 4-D Nova. Not being a=20
specialist on either series, I took the owner's word for it.
Ray
=20
On Mon, Aug 10, 2015 at 12:15 PM, _PLMossman@aol.com_=20
(mailto:PLMossman@aol.com) [colonial-coins] wrote:=20=20
Hello All:
May I ask, what is the current 1788 CT variety over a NOVA host coin?=20=20
There are eight 1788 CT varieties occasionally to always found on NOVA hos=
ts.
=20
I've been maintaining a census of all overstruck state coppers [see CNL=20
pp. 2977-82] For the 1788 CTs, I've been searching for another 1788 11-G =
o/s=20
on a NOVA. I have one but sometime in the past [10=C2=B1 years] another w=
as=20
said to have been shown at a November Boston C4 meeting. I've not been ab=
le=20
to verify it and no one else I've consulted remembers it. Is this=20
possibly one?=20=20
Best
Phil Mossman
=20
=20
In a message dated 8/10/2015 10:16:16 A.M. Eastern Daylight Time,=20
_colonial-coins@yahoogroups.com_ (mailto:colonial-coins@yahoogroups.com) =
writes:
=20
Yes Gary,=20=20
An image of a 1788 CT Copper struck over a 1785 Nova Constellatio was=20
posted on the EAC facebook site called Coppernotes. It has generated some=
=20=20
nice comments. I think that the EAC members that specialize in Half Cents=
and=20
Cents have an appreciation for our colonials, even if they don't collect=20
them.
Ray
=20
On Mon, Aug 10, 2015 at 10:10 AM, Gary Smith _Gry1564@aol.com_=20
(mailto:Gry1564@aol.com) [colonial-coins] wrote:=20=20
Lots of 'noise' on the EAC CopperNotes site folks! :-)=20=20=20
Gary
Sent from AOL Mobile Mail
-----Original Message-----
From: Ray Williams _njraywms@optonline.net_=20
(mailto:njraywms@optonline.net) [colonial-coins] <_colonial-coins@yahoogr=
oups.com_=20
(mailto:colonial-coins@yahoogroups.com) >
To: _colonial-coins@yahoogroups.com_=20
(mailto:colonial-coins@yahoogroups.com) _colonial-coins@yahoogroups.com_=
=20
(mailto:colonial-coins@yahoogroups.com) <_colonial-coins@yahoogroups.com_=
=20
(mailto:colonial-coins@yahoogroups.com) >
Cc: _colonial-coins@yahoogroups.com_=20
(mailto:colonial-coins@yahoogroups.com) _colonial-coins@yahoogroups.com_=
=20
(mailto:colonial-coins@yahoogroups.com) <_colonial-coins@yahoogroups.com_=
=20
(mailto:colonial-coins@yahoogroups.com) >
Sent: Mon, Aug 10, 2015 07:14 AM
Subject: RE: [Colonial Numismatics] for CT Copper Collectors
=20
=20
=20
=20
Beauty is in the eye of the beholder.=20
Having a little fun with my CT Copper friends.=20
But undertypes are fun.=20
Ray=20
=20
On Sun, Aug 09, 2015 at 09:39 PM, Robert Martin _robertmartin22@live.com_=
=20
(mailto:robertmartin22@live.com) [colonial-coins] wrote:=20=20
Ray,=20
I don't think an R1 NJ overstruck on a R6/R7 Ct is an improvement.=20
Although, you are right, that colonial and state copper overstrikes are =
=20
fascinating and interesting to collect.=20
Robert=20=20
=20
____________________________________
To: _colonial-coins@yahoogroups.com_=20
(mailto:colonial-coins@yahoogroups.com)=20=20=20
From: _colonial-coins@yahoogroups.com_=20
(mailto:colonial-coins@yahoogroups.com)=20=20=20
Date: Sun, 9 Aug 2015 20:46:12 -0400=20
Subject: [Colonial Numismatics] for CT Copper Collectors=20=20
=20
Hi Guys,=20=20
A suggestion for a collecting direction as your collecting=20
direction might change... Consider collecting as many CT Copper=20=20
varieties as you can, that have been improved by NJ Copper dies. In all=20
seriousness, I do find undertypes fascinating and I like to obtain=20
interesting ones.=20=20
It's been quiet here lately.=20
Ray=20
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<DIV>Explanation of Student's T test: </DIV>
<DIV><EM></EM> </DIV>
<DIV><EM>Start: </EM>"The <A title=3DT-statistic=20
href=3D"https://en.wikipedia.org/wiki/T-statistic"><EM>t</EM>-statistic</A>=
was=20
introduced in 1908 by <A title=3D"William Sealy Gosset"=20
href=3D"https://en.wikipedia.org/wiki/William_Sealy_Gosset">William Sealy=20
Gosset</A>, a chemist working for the <A title=3DGuinness=20
href=3D"https://en.wikipedia.org/wiki/Guinness">Guinness</A> <A title=3DBre=
wery=20
href=3D"https://en.wikipedia.org/wiki/Brewery">brewery</A> in <A title=3DDu=
blin=20
href=3D"https://en.wikipedia.org/wiki/Dublin">Dublin</A>, <A title=3DIrelan=
d=20
href=3D"https://en.wikipedia.org/wiki/Ireland">Ireland</A>" (<FONT=20
color=3D#ff0000>Student</FONT> was his <A title=3D"Pen name"=20
href=3D"https://en.wikipedia.org/wiki/Pen_name">pen name</A>) [A fascinatin=
g=20
story] </DIV>
<DIV> </DIV>
<DIV>The Student's t test is widely used in medicine and elsewhere to deter=
mine=20
the effectiveness of new procedures - whether one medicine,=20
procedure, or treatment, etc. is better than a control or the "ol=
d=20
way." A t test value of 1.0 =3D identical results; values from 0=
.999 to=20
0.051 mean the two comparisons are similar, or you can't be sure the values=
are=20
different or that your new idea is working.</DIV>
<DIV>But a value of 0.05 level or smaller is a <FONT=20
style=3D"BACKGROUND-COLOR: #ffff00">positive result</FONT> that the <FONT=20
style=3D"BACKGROUND-COLOR: #ffff00">compared entities are different</FONT> =
- or=20
that the new procedure is working, etc.</DIV>
<DIV> </DIV>
<DIV>So in discussing the relative weights of [96] 1783 and [165] 178=
5=20
Novas, I took my data from pages 141-44, note 186, and Table 5.5<EM> =
From=20
Crime to Punishment.</EM></DIV>
<DIV><EM></EM> </DIV>
<DIV><FONT style=3D"BACKGROUND-COLOR: #ffff00">Quote</FONT> "The important =
thing=20
to note is that these nine varieties of Nova coppers were not consistently=
=20
struck from the same planchet stock. Absence of a homogeneous weight sugges=
ts no=20
common weight standard with the 1783-dated group being significantly heavie=
r=20
that the 1785 varieties." </DIV>
<DIV> </DIV>
<DIV><FONT style=3D"BACKGROUND-COLOR: #ffff00">See Table 5.5, [copied below=
] where=20
I asked statistically two questions about 1785 4-D.</FONT></DIV>
<DIV><FONT style=3D"BACKGROUND-COLOR: #00ffff"><STRONG>First:</STRONG> whet=
her the=20
average weights of 1785 4-D <STRONG>[124.52 =C2=B1 7.37]</STRONG> is =
similar to=20
the three in the 1783 group, <STRONG>[123.69 =C2=B1=20
10.70</STRONG>.],</FONT></DIV>
<DIV><FONT style=3D"BACKGROUND-COLOR: #00ffff">Answer: Student=E2=80=
=99s T test: p =3D=20
0.72</FONT>; </DIV>
<DIV>p means probability.</DIV>
<DIV><EM><STRONG><FONT style=3D"BACKGROUND-COLOR: #00ffff">Answer:=20
</FONT></STRONG></EM><EM><STRONG><FONT style=3D"BACKGROUND-COLOR: #00ffff">=
First=20
Question</FONT></STRONG>: </EM> </DIV>
<DIV>
<P style=3D"MARGIN: 0in 0in 0pt" class=3DMsoFootnoteText><FONT=20
style=3D"BACKGROUND-COLOR: #00ffff">That means that there are 72 chances in=
100=20
that 1785 4-D and all of 1783 Nova are the same weight. [Read ?? mayb=
e the=20
same planchet stock,] </FONT><FONT=20
style=3D"BACKGROUND-COLOR: #00ffff"></FONT></P>
<DIV><FONT style=3D"BACKGROUND-COLOR: #ffff80"><EM><STRONG>Second=20
question:</STRONG></EM> whether 4-D, <STRONG>124.52 =C2=B1 7.37,</STRO=
NG> was=20
similar in weight to other<SPAN=20
style=3D"FONT-FAMILY: 'Times New Roman'; FONT-SIZE: 12pt"><SPAN>=20
<STRONG>five</STRONG> </SPAN>1785-dated varieties,=20
<STRONG>[115.0=C2=B16.8]</STRONG> Student=E2=80=99s T test:<STRONG>=20
</STRONG></SPAN><SPAN=20
style=3D"FONT-FAMILY: 'Times New Roman'; FONT-SIZE: 12pt"><STRONG>p =3D 1.7=
x=20
10<SUP>-9</SUP>.</STRONG></SPAN></FONT></DIV>
<P style=3D"MARGIN: 0in 0in 0pt" class=3DMsoFootnoteText><FONT=20
style=3D"BACKGROUND-COLOR: #ffff80"><SPAN=20
style=3D"FONT-FAMILY: 'Times New Roman'; FONT-SIZE: 12pt"></SPAN></FONT>&nb=
sp;</P>
<P style=3D"MARGIN: 0in 0in 0pt" class=3DMsoFootnoteText><SPAN=20
style=3D"FONT-FAMILY: 'Times New Roman'; FONT-SIZE: 12pt"><FONT=20
style=3D"BACKGROUND-COLOR: #ffff80"><EM>Answer</EM> - Student=E2=80=99s T t=
est: p =3D 1.7 x=20
10<SUP>-9</SUP>.</FONT></SPAN></P>
<P style=3D"MARGIN: 0in 0in 0pt" class=3DMsoFootnoteText><FONT=20
style=3D"BACKGROUND-COLOR: #ffff80">That means that the likelihood of =
the=20
average weights of the single 1785 group 4-D being similar to the=20
other</FONT><SPAN style=3D"FONT-FAMILY: 'Times New Roman'; FONT-SIZE: 12pt"=
><FONT=20
style=3D"BACKGROUND-COLOR: #ffff80"><SPAN> five </SPAN>1785 varieties is=20
0.00000000017 chances. Pretty slim pickins!</FONT> </SPAN></P>
<P style=3D"MARGIN: 0in 0in 0pt" class=3DMsoFootnoteText><SPAN=20
style=3D"FONT-FAMILY: 'Times New Roman'; FONT-SIZE: 12pt"><FONT=20
style=3D"BACKGROUND-COLOR: #ffff80"></FONT></SPAN> </P>
<P style=3D"MARGIN: 0in 0in 0pt" class=3DMsoFootnoteText><SPAN=20
style=3D"FONT-FAMILY: 'Times New Roman'; FONT-SIZE: 12pt"><FONT=20
style=3D"BACKGROUND-COLOR: #ffffff">I am not a mathematician - I have frien=
ds who=20
are and I just love Microsoft Excel!! I've told you all I=20
know.</FONT></SPAN></P>
<P style=3D"MARGIN: 0in 0in 0pt" class=3DMsoFootnoteText><SPAN=20
style=3D"FONT-FAMILY: 'Times New Roman'; FONT-SIZE: 12pt"></SPAN> </P>
<P style=3D"MARGIN: 0in 0in 0pt" class=3DMsoFootnoteText><SPAN=20
style=3D"FONT-FAMILY: 'Times New Roman'; FONT-SIZE: 12pt">Enjoy, </SPAN></P=
>
<P style=3D"MARGIN: 0in 0in 0pt" class=3DMsoFootnoteText><SPAN=20
style=3D"FONT-FAMILY: 'Times New Roman'; FONT-SIZE: 12pt">Phil </SPAN>=
</P></DIV>
<DIV> </DIV>
<DIV>
<DIV>In a message dated 8/11/2015 7:52:20 A.M. Eastern Daylight Time,=20
colonial-coins@yahoogroups.com writes:</DIV>
<BLOCKQUOTE=20
style=3D"BORDER-LEFT: blue 2px solid; PADDING-LEFT: 5px; MARGIN-LEFT: 5px">=
<FONT=20
style=3D"BACKGROUND-COLOR: transparent" color=3D#000000 size=3D2 face=3DA=
rial><SPAN=20
style=3D"DISPLAY: none"> </SPAN>=20
<DIV id=3Dygrp-text>
<P>Thanks Craig,=20
<DIV> That link about Student t-test makes it=20
perfectly clear... NOT! It's Greek to me. Knowing it's =
some=20
statistical formula, any attempt to explain is probably useless. Te=
lling=20
me that the difference between the average of two varieties is X grains o=
r is=20
6% would be something I can comprehend. </DIV>
<DIV>Ray </DIV>
<DIV style=3D"FONT-FAMILY: Verdana">
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>On Mon, Aug 10, 2015 at 10:47 PM, Cmcdon0923=20
CMcdon0923@aol.com [colonial-coins] wrote:=20
<DIV> </DIV>
<DIV> </DIV>
<BLOCKQUOTE=20
style=3D"BORDER-LEFT: rgb(136,136,136) 2px solid; MARGIN: 0pt 0pt 0pt 0.8=
ex"><BR><BR>
<DIV>Yeah.....this makes it so much clearer ..... </DIV>
<DIV><BR></DIV>
<DIV>
<DIV><A title=3D"https://en.m.wikipedia.org/wiki/Student's_t-test"=20
href=3D"https://en.m.wikipedia.org/wiki/Student%27s_t-test"=20
target=3D_blank><FONT=20
color=3D#000000>https://en.m.wikipedia.org/wiki/Student%27s_t-test</FON=
T></A></DIV>
<DIV><BR></DIV>
<DIV><SPAN><BR></SPAN></DIV></DIV>
<DIV>Sent from my iPhone.....so spelling doens't count. </DIV>
<DIV><BR>On Aug 10, 2015, at 9:17 PM, Ray Williams <A=20
title=3Dmailto:njraywms@optonline.net=20
href=3D"mailto:njraywms@optonline.net">njraywms@optonline.net</A>=20
[colonial-coins] <<A title=3Dmailto:colonial-coins@yahoogroups.com=20
href=3D"mailto:colonial-coins@yahoogroups.com">colonial-coins@yahoogrou=
ps.com</A>>=20
wrote:<BR><BR></DIV>
<BLOCKQUOTE type=3D"cite">
<DIV><SPAN> </SPAN>=20
<DIV id=3Dygrp-text>
<P>Okay,</P>
<DIV> I'll bite... What is a Student's =
T=20
test? Is this a statistical term that I won't understand, not b=
eing=20
a statistician?</DIV>
<DIV>Ray</DIV>
<DIV style=3D"FONT-FAMILY: Verdana">
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>On Mon, Aug 10, 2015 at 09:02 PM, <A=20
title=3Dmailto:PLMossman@aol.com=20
href=3D"mailto:PLMossman@aol.com">PLMossman@aol.com</A> [colonial-coi=
ns]=20
wrote:=20
<DIV> </DIV>
<DIV> </DIV>
<BLOCKQUOTE=20
style=3D"BORDER-LEFT: rgb(136,136,136) 2px solid; MARGIN: 0pt 0pt 0pt=
0.8ex"><BR><BR><FONT=20
color=3D#000000 size=3D3 face=3D"Times New Roman"></FONT>
<DIV>Hi Will:</DIV>
<DIV>My numbers re: undertypes are just statistical guesses - =
since=20
the 20 identifiable undertypes are too few to make positive=20
statements. </DIV>
<DIV> </DIV>
<DIV>In my Table 5.5 in <EM>From Crime to Punishment</EM>, I was ab=
le to=20
gather over the years weight stats on 96 1783s, and 165 1785s that =
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